Solution of a class of vibration problems by flowgraph methods

A 4-degree-of-freedom single-input system and a 3-degree-of-freedom multi-input system are solved by the Coates', modified Coates' and Chan-Mai flowgraph methods. It is concluded that the Chan-Mai flowgraph method is superior to other flowgraph methods in such cases.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Response of Circular Footings to Vertical Vibrations

In this paper, analog solutions are presented for the response of a circular footing resting on an elastic half-space with uniform and parabolic contact pressure distributions and subjected to frequency dependent and frequency independent excitations. In addition, an analog solution to a rigid circular footing subjected to frequency dependent excitation is also presented. The results have been compared with the rigorous solution of Sung and the agreement is found to be good.

Solution of a generalized Korteweg-de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

A Convenient Route for the Synthesis of Complex Metal Oxides Employing Solid-Solution Precursors

Synthesis of complex metal oxides by the thermal decomposition of solid-solution precursors (formed by isomorphous compounds of component metals) has been investigated since the method enables mixing of cations on an atomic scale and drastically reduces diffusion distances to a few angstroms. Several interesting oxides such as Ca2Fe03,5C, aCoz04,C a2C0205a, nd Ca,FeCo05 have been prepared by this technique starting from carbonate solid solutions of the type Ca,-,Fe,C03, Cal-,Co,C03, and Ca,-,,M,M'yC03 (M, M' = Mn, Fe, Co). The method has been extended to oxalate solid-solution precursors, and the possibility of making use of other kinds of precursor solid solutions is indicated.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

A Decentralized Session Management Framework for Heterogeneous Ad-Hoc and Fixed Networks

Wireless technologies are continuously evolving. Second generation cellular networks have gained worldwide acceptance. Wireless LANs are commonly deployed in corporations or university campuses, and their diffusion in public hotspots is growing. Third generation cellular systems are yet to affirm everywhere; still, there is an impressive amount of research ongoing for deploying beyond 3G systems. These new wireless technologies combine the characteristics of WLAN based and cellular networks to provide increased bandwidth. The common direction where all the efforts in wireless technologies are headed is towards an IP-based communication. Telephony services have been the killer application for cellular systems; their evolution to packet-switched networks is a natural path. Effective IP telephony signaling protocols, such as the Session Initiation Protocol (SIP) and the H 323 protocol are needed to establish IP-based telephony sessions. However, IP telephony is just one service example of IP-based communication. IP-based multimedia sessions are expected to become popular and offer a wider range of communication capabilities than pure telephony. In order to conjoin the advances of the future wireless technologies with the potential of IP-based multimedia communication, the next step would be to obtain ubiquitous communication capabilities. According to this vision, people must be able to communicate also when no support from an infrastructured network is available, needed or desired. In order to achieve ubiquitous communication, end devices must integrate all the capabilities necessary for IP-based distributed and decentralized communication. Such capabilities are currently missing. For example, it is not possible to utilize native IP telephony signaling protocols in a totally decentralized way. This dissertation presents a solution for deploying the SIP protocol in a decentralized fashion without support of infrastructure servers. The proposed solution is mainly designed to fit the needs of decentralized mobile environments, and can be applied to small scale ad-hoc networks or also bigger networks with hundreds of nodes. A framework allowing discovery of SIP users in ad-hoc networks and the establishment of SIP sessions among them, in a fully distributed and secure way, is described and evaluated. Security support allows ad-hoc users to authenticate the sender of a message, and to verify the integrity of a received message. The distributed session management framework has been extended in order to achieve interoperability with the Internet, and the native Internet applications. With limited extensions to the SIP protocol, we have designed and experimentally validated a SIP gateway allowing SIP signaling between ad-hoc networks with private addressing space and native SIP applications in the Internet. The design is completed by an application level relay that permits instant messaging sessions to be established in heterogeneous environments. The resulting framework constitutes a flexible and effective approach for the pervasive deployment of real time applications.

Effective earth and space science analogies

There are several good reasons why Earth and Space Science should be a part of any science curriculum. Nearly everything we do each day is connected in some way to the Earth: to its land, oceans, atmosphere, plants and animals. By 2025, eight billion people will live on Earth. If we are to continue extracting resources to maintain a high quality of life, then it is important that our children are scientifically literate in a way that allows them to exploit the Earth’s resources in a sustainable way. People who understand how earth systems work can make informed decisions and may be able to help resolve issues surrounding clean water, urban planning and development, global climate change and the use and management of natural resources.

Efficient search for statistically significant dependency rules in binary data

Analyzing statistical dependencies is a fundamental problem in all empirical science. Dependencies help us understand causes and effects, create new scientific theories, and invent cures to problems. Nowadays, large amounts of data is available, but efficient computational tools for analyzing the data are missing. In this research, we develop efficient algorithms for a commonly occurring search problem - searching for the statistically most significant dependency rules in binary data. We consider dependency rules of the form X->A or X->not A, where X is a set of positive-valued attributes and A is a single attribute. Such rules describe which factors either increase or decrease the probability of the consequent A. A classical example are genetic and environmental factors, which can either cause or prevent a disease. The emphasis in this research is that the discovered dependencies should be genuine - i.e. they should also hold in future data. This is an important distinction from the traditional association rules, which - in spite of their name and a similar appearance to dependency rules - do not necessarily represent statistical dependencies at all or represent only spurious connections, which occur by chance. Therefore, the principal objective is to search for the rules with statistical significance measures. Another important objective is to search for only non-redundant rules, which express the real causes of dependence, without any occasional extra factors. The extra factors do not add any new information on the dependence, but can only blur it and make it less accurate in future data. The problem is computationally very demanding, because the number of all possible rules increases exponentially with the number of attributes. In addition, neither the statistical dependency nor the statistical significance are monotonic properties, which means that the traditional pruning techniques do not work. As a solution, we first derive the mathematical basis for pruning the search space with any well-behaving statistical significance measures. The mathematical theory is complemented by a new algorithmic invention, which enables an efficient search without any heuristic restrictions. The resulting algorithm can be used to search for both positive and negative dependencies with any commonly used statistical measures, like Fisher's exact test, the chi-squared measure, mutual information, and z scores. According to our experiments, the algorithm is well-scalable, especially with Fisher's exact test. It can easily handle even the densest data sets with 10000-20000 attributes. Still, the results are globally optimal, which is a remarkable improvement over the existing solutions. In practice, this means that the user does not have to worry whether the dependencies hold in future data or if the data still contains better, but undiscovered dependencies.

Crystal and molecular structure of allo-4-hydroxy-L-proline dihydrate

allo-4-Hydroxy-L-proline crystallizes from an aqueous solution as the dihydrate. The crystals are orthorhombic, space group P212121, with a=7.08 (2), b=22.13 (3), c= 5"20 (2) A,. The structure was solved by direct methods and refined by block-diagonal least squares. The final R for 733 observed reflexions is 0.054. The molecule exists as a zwitterion with hydroxyl and carboxyl groups cis to the pyrrolidine ring. The latter is puckered at the fl-carbon atom, which deviates by -0.54 A, from the best plane formed by the four remaining atoms. The molecules are held together by a network of hydrogen bonds, the water molecules playing a dominant role in the stability of the structure.

Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.

Kinetics of resinification of furfuryl alcohol in aqueous solution

Kinetic information on the resinification of furfuryl alcohol has been derived from the rate of increase of color intensity measured with a photoelectric colorimeter, the resinification being carried out isothermally in Clark-Lubs aqueous buffer solutions in the pH range of 1.0-2.2. The activation energy for polymerization is found to increase exponentially with pH. The time required for emulsification (which is quickly followed by separation of resin layer) to occur in an aqueous solution of furfuryl alcohol also increases exponentially with pH, but it decreases exponentially with temperature. This is described quantitatively by a single expression.

Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m times n) matrix with non-negative elements, x and g are respectively (n times 1) and (m times 1) vectors with positive components.